// Runge-Kutta 4 solver of 1st order ODE
#include <stdio.h>
#include <math.h>

double f(double t, double y);
double analyticalsol(double x);
void RK4(double dt, double t0, double y0, double tmax);
void plotfunction(double x0, double x1, int N);

// Driver program
int main() 
{ 
    // Initial values
    RK4(0.5,0.0,1.0,50); 
    plotfunction(0.0, 50,1000);
    return 0; 
} 


void RK4(double dt, double t0, double y0, double tmax) 
{ 
   double y,t,k1,k2,k3,k4;
   FILE *output;

   output = fopen("RK4.dat", "w");//opening file. 

    t=t0;
    y=y0;
    fprintf(output,"%.15f\t%.15f\n",t0,y0);

    while (t <= tmax) 
    { 
        k1=dt*f(t,y);
        k2=dt*f(t+0.5*dt,y+0.5*k1);
        k3=dt*f(t+0.5*dt,y+0.5*k2);
        k4=dt*f(t+dt,y+k3);

       y=y+(k1+2.0*k2+2.0*k3+k4)/6.0; 
       t=t+dt;
      fprintf(output,"%.15f\t%.15f\n",t,y);

    } 
     fclose(output);//closing file.

} 


void plotfunction(double x0, double x1,int N)
{ int i;
  double x,dx;
  FILE *output;

      dx=(x1-x0)/N;


output = fopen("function.dat", "w");//opening file. 
 for(i=0;i<N;i++){
    x=x0+dx*i;
fprintf(output,"%.15f\t%.15f\n",x,analyticalsol(x));
 }
 
 fclose(output);//closing file.

}


// Define function

double f(double t, double y) 
{ 
    double fun;

fun=-10*y;
    return fun;
} 

double analyticalsol(double x) 
{ 
    double y;

y=exp(-10*x);
    return y;
}